This should help you
{{ if eq .Section "vX.Y" }} <----- override global version site param ----->{{ end }}
Note that this will affect all pages in this section.
As for getting the parameter through a shortcode I’ve only had a need to do this from the first parent page.
So I haven’t tried going higher up.
But someone else has tried. See: Nested Shortcodes - Get Furthest/Farthest Parent Param